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Hint: In order to solve this problem assume a term to be zero and then find the number of that term. Get the first term, common difference from the AP given.

Complete step-by-step answer:

The given AP is 21,18,15,..............

We can clearly see first term is ${{\text{a}}_1}$= 21 = a â€¦â€¦(1)

And common difference can be calculated as ${{\text{a}}_2}$ - ${{\text{a}}_1}$=d

So from the AP we can say ${{\text{a}}_2}$ = 18

Therefore, d = 18 â€“ 21 = -3 â€¦â€¦(2)

So, d = -3

Let us assume the nth term to be 0.

Then, ${{\text{a}}_{\text{n}}}$= 0 â€¦â€¦(3)

We know ${{\text{a}}_{\text{n}}}$= a+(n-1)d

So we can do,

${{\text{a}}_{\text{n}}}$= 21+(n-1)(-3)=0 â€¦â€¦(From (1), (2) and (3))

21 + -3n+3=0

24=3n

n = $\dfrac{{24}}{3}$

n = 8.

Hence, the 8th term of the AP is Zero.

Note: Whenever you face such types of problems obtain the first term and common difference from the given AP. Here in this question we have assumed the nth term to be zero then we have applied the formula of nth term of the AP. Proceeding like this you will get the right solution.

Complete step-by-step answer:

The given AP is 21,18,15,..............

We can clearly see first term is ${{\text{a}}_1}$= 21 = a â€¦â€¦(1)

And common difference can be calculated as ${{\text{a}}_2}$ - ${{\text{a}}_1}$=d

So from the AP we can say ${{\text{a}}_2}$ = 18

Therefore, d = 18 â€“ 21 = -3 â€¦â€¦(2)

So, d = -3

Let us assume the nth term to be 0.

Then, ${{\text{a}}_{\text{n}}}$= 0 â€¦â€¦(3)

We know ${{\text{a}}_{\text{n}}}$= a+(n-1)d

So we can do,

${{\text{a}}_{\text{n}}}$= 21+(n-1)(-3)=0 â€¦â€¦(From (1), (2) and (3))

21 + -3n+3=0

24=3n

n = $\dfrac{{24}}{3}$

n = 8.

Hence, the 8th term of the AP is Zero.

Note: Whenever you face such types of problems obtain the first term and common difference from the given AP. Here in this question we have assumed the nth term to be zero then we have applied the formula of nth term of the AP. Proceeding like this you will get the right solution.

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